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  4. An ideal diatomic gas is heated at constant pressure. The ratio of the work done to the heat supplied is

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Q. An ideal diatomic gas is heated at constant pressure. The ratio of the work done to the heat supplied is

KVPYKVPY 2009Thermodynamics

Solution:

Heat supplied at constant pressure is $\Delta Q =n C_{p}\Delta T$
Work done by the gas,
$\Delta W =p\Delta V=nR\Delta T$
Ratio of work done to heat supplied is
$\frac{\Delta W}{\Delta Q}=\frac{nR\Delta T}{nC_{p}\Delta T}$
$=\frac{R}{C_{p}}=\frac{C_{p}-C_{V}}{C_{p}}$
$=1-\frac{1}{\gamma}$
$=1-\frac{1}{\left(7 /5\right)}$
$=1-\frac{5}{7}=\frac{2}{7}$